What’s the difference between these terms? You see them frequently, especially in auction catalogs.
I’m not sure there is an official philatelic distinction. But here is my opinion and I think it reflects reality.
Collections are highly organized. There is little, if any, duplication of material. There is one of each item (stamp, cover, plate block, etc.). If there is any duplication of material, it’s generally very light.
Some collections are very specialized, such as a collection of US Scott #11. In this case, yes, there are many “duplicates” if you just look at the stamp. However, the collection is all different because there are green cancels, red cancels, fancy cancels, usages on Express covers, plate varieties, pairs, blocks, and so forth. Viewed that way, then the collection really is made up of all different material.
Accumulations and mixtures have varying degrees of duplication. The main difference is in organization.
Accumulations usually have some degree of organization around them. Stamps are usually separated by Scott number or country. Mint and used are separated too. Duplication can be light (few copies per Scott #) to heavy (hundreds or thousands of copies per Scott #). Accumulations may be organized by glassine envelopes, stock books, cigar boxes, or other ways of separating material. Accumulations can be small (a stockbook or cigar box of material) to huge (a roomful of stamps within many file cabinets). With an accumulation, you have some idea of what you are buying (mint, used, or both; which countries are involved, and so forth). An example of an accumulation is, “Scott #803-832. 5000+ items stored on stock pages. 80% used. A few scattered MNH plate blocks on the low values. Up to 300 used copies per Scott #.” Reading that, it should be very clear what you’re buying.
To me, a stock is similar to an accumulation with two differences. The first difference is that duplication is light, overall. There may be a dozen or less copies of any one item. You usually don’t find hundreds or thousands of an item in a stock. Second, a stock is more highly organized than an accumulation. Many times these items came from another dealer and they are sorted on to sales cards (or something similar) and they are almost ready for sale. Usually accumulations aren’t as highly organized and not really ready for immediate (or near immediate) sale. Stocks are more targeted towards a dealer buying them, and not really a collector.
Mixtures typically have little, if any, organization. Mixtures can be small in size (e.g., cigar box) or large (boxes weighing many pounds with many thousands of stamps).Often with mixtures, you have no idea what you’re getting which is part of the fun. You might run into a more valuable item that was buried amongst more common material. An example description is “Mixture of 100,000 used US, off paper stamps from 1920s-1930s stored in 5 banker boxes.” The stamps will be all out of order. In this case, you may find a Scott #1 in the mixture, or not. Mixtures often have moderate to heavy duplication. There could be hundreds or more of any Scott number in a mixture. .